Question

For a profit maximising monopolist, the ratio of the profit margin to price (also known as the Lerner Index or the relative mark-up) has a relationship with the price-elasticity of demand at the profit maximising price. Then, which of the following statements is CORRECT?

• A. The larger the elasticity of demand at the profit maximising price, the greater is the relative mark-up
• B. The power to sustain a price higher than the marginal cost depends only on the profit maximising price
• C. At the profit maximising price, given costs are greater than zero, the price elasticity of demand is strictly larger than unity
• D. At the revenue maximising price, the price elasticity of demand is greater than unity

Answer 1

The Correct Option is C

The Lerner Index and Monopolist’s Pricing Power

The Lerner Index, which measures a monopolist’s pricing power, is defined as: 

L = (P - MC) / P = 1 / |E_d|

Where:

• P = Price
• MC = Marginal Cost
• E_d = Price Elasticity of Demand

Profit Maximization Condition

• For a profit-maximizing monopolist, the demand elasticity must be greater than one in absolute terms, i.e., |E_d| > 1.
• This ensures that P > MC, meaning the monopolist has pricing power.
• If |E_d| ≤ 1, then marginal revenue becomes non-positive, which contradicts the requirement for profit maximization.

Implication of |E_d| > 1

• The condition |E_d| > 1 guarantees that the Lerner Index is positive, meaning:
• (P - MC) / P > 0, which implies a positive profit margin.

Conclusion

For a monopolist to maximize profit, the absolute value of demand elasticity must be greater than one (|E_d| > 1), ensuring P > MC and a positive Lerner Index.